Authorised by Academic Registrar, April 1996
Objectives This subject aims to develop an understanding of the process of mathematical modelling, and for students to master the details of certain established, continuous models drawn from the physical sciences; use a variety of techniques from single-variable calculus to solve mathematical formulations of physical models (particularly cases based on differential equations), and to explore the assumptions and predictions of these models; teach students to carry out the full process of formulating a simple mathematical model, using an outline `recipe' for the process.
Synopsis This subject is designed to help students to develop some skill in the craft of mathematical modelling, and to introduce several continuous mathematical models from the physical sciences. This subject provides an introduction to the craft of selecting, constructing, analysing and criticising mathematical models. Selected case studies drawn from areas such as population dynamics, animal and plant growth and planetary motion are included. The main emphasis, however, is on students' attempts at formulating their own models in assignment work. Therefore, general procedures and advice on model formulation are provided, and the case studies are intended to illustrate principles which students may apply in their own work. Some general concepts used in analysing physical systems, such as those of conservation laws, interactions and rate equations are discussed. Simple methods from calculus are used to solve and analyse many of the models introduced. For on-campus students the subject is taught by lectures and tutorials, with opportunities for class discussion and class modelling investigations. Some established models are also explained and criticised (problem sets on these are set for exam preparation but not for assessment).
Assessment Three modelling assignments: 60% + Examination: 40%